The Airport definitely needs more than one public transport systems.

1) The Finnair bus might be the best, if you are going where it stops and don't want to spend 40-45€ for taxi
2) Train is by far the best for locals, who live near the stations like I do

One huge problem with the train? If there is a train connection, I don't want to stare at the timetable before every trip. Some examples: On Sunday the first train arrives to airport at 0616, there are about 20 flights leaving between 0600-0700. On Sunday the last train from the airport leaves at 2327. Do not try to catch it if you are coming for example from AY/BA LHR evening flights.

They should have 1-2 more trains every 30min in these times so that at least almost every flight would have a connection.